Skip to main content
SpringerLink
Log in

The dissipative Bose-Hubbard model

Methods and examples

  • Review
  • Published:
The European Physical Journal Special Topics Aims and scope Submit manuscript

Abstract

Open many-body quantum systems have attracted renewed interest in the context of quantum information science and quantum transport with biological clusters and ultracold atomic gases. The physical relevance in many-particle bosonic systems lies in the realization of counter-intuitive transport phenomena and the stochastic preparation of highly stable and entangled many-body states due to engineered dissipation. We review a variety of approaches to describe an open system of interacting ultracold bosons which can be modeled by a tight-binding Hubbard approximation. Going along with the presentation of theoretical and numerical techniques, we present a series of results in diverse setups, based on a master equation description of the dissipative dynamics of ultracold bosons in a one-dimensional lattice. Next to by now standard numerical methods such as the exact unravelling of the master equation by quantum jumps for small systems and beyond mean-field expansions for larger ones, we present a coherent-state path integral formalism based on Feynman-Vernon theory applied to a many-body context.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. E.A. Cornell, C.E. Wieman, Rev. Mod. Phys. 74, 875 (2002)

    Article  ADS  Google Scholar 

  2. W. Ketterle, Rev. Mod. Phys. 74, 1131 (2002)

    Article  ADS  Google Scholar 

  3. M. Albiez, R. Gati, J. Fölling, S. Hunsmann, M. Cristiani, M.K. Oberthaler, Phys. Rev. Lett. 95, 010402 (2005)

    Article  ADS  Google Scholar 

  4. C. Gross, T. Zibold, E. Nicklas, J. Estève, M.K. Oberthaler, Nature 464, 1165 (2010)

    Article  ADS  Google Scholar 

  5. W.S. Bakr, J.I. Gillen, A. Peng, S. Foelling, M. Greiner, Nature 462, 74 (2009)

    Article  ADS  Google Scholar 

  6. M. Miranda, R. Inoue, Y. Okuyama, A. Nakamoto, M. Kozuma, Phys. Rev. A 91, 063414 (2015)

    Article  ADS  Google Scholar 

  7. J.F. Sherson, C. Weitenberg, M. Endres, M. Cheneau, I. Bloch, S. Kuhr, Nature 467, 68 (2010)

    Article  ADS  Google Scholar 

  8. C. Weitenberg, M. Enders, J.F. Sherson, M. Cheneau, P. Schauß, T. Fukuhara, I. Bloch, S. Kuhr, Nature 471, 319 (2011)

    Article  ADS  Google Scholar 

  9. R. Labouvie, B. Santra, S. Heun, S. Wimberger, H. Ott, Phys. Rev. Lett. 115, 05060 (2015)

    Article  Google Scholar 

  10. T. Gerike, P. Würtz, D. Reitz, T. Langen, H. Ott, Nature Phys. 4, 949 (2008)

    Article  ADS  Google Scholar 

  11. J. Hubbard, Proceedings of the Royal Society of London 276, 238 (1963)

  12. R. Grimm, M. Weidemüller, Y.B. Ovchinnikov, Adv. Atom. Mol. Opt. Phys. 42, 95 (2000)

    Article  ADS  Google Scholar 

  13. O. Morsch, M. Oberthaler, Rev. Mod. Phys. 78, 179 (2006)

    Article  ADS  Google Scholar 

  14. I. Bloch, J. Dalibard, W. Zwerger, Rev. Mod. Phys. 80, 885 (2008)

    Article  ADS  Google Scholar 

  15. M. Lewenstein, A. Sanpera, V. Ahufinger, B. Damski, A. Sen(De), U. Sen, Adv. Phys. 56, 243 (2007)

    Article  ADS  Google Scholar 

  16. T. Langen, et al., Science 348, 207 (2015)

    Article  MathSciNet  ADS  Google Scholar 

  17. S. Braun, et al., PNAS 112, 3641 (2015)

    Google Scholar 

  18. J.P. Brantut, J. Meineke, D. Stadler, S. Krinner, T. Esslinger, Science 337, 1069 (2012)

    Article  ADS  Google Scholar 

  19. S. Eckel, J.G. Lee, F. Jendrzejewski, N. Murray, C.W. Clark, C.J. Lobb, W.D. Phillips, M. Edwards, G.K. Campbell, Nature 506, 200 (2014)

    Article  ADS  Google Scholar 

  20. I. Bloch, J. Dalibard, S. Nascimbene, Nat. Phys. 8, 267 (2012)

    Article  Google Scholar 

  21. M.P.A. Fisher, P.B. Weichman, G. Grinstein, D.S. Fisher, Phys. Rev. B 40, 546 (1989)

    Article  ADS  Google Scholar 

  22. D. Jaksch, C. Bruder, J.I. Cirac, C.W. Gardiner, P. Zoller, Phys. Rev. Lett. 81, 3108 (1998)

    Article  ADS  Google Scholar 

  23. D. Jaksch, P. Zoller, Ann. Phys. 315, 52 (2005)

    Article  MATH  ADS  Google Scholar 

  24. A. Tomadin, S. Diehl, M.D. Lukin, P. Rabl, P. Zoller, Phys. Rev. A 86, 033821 (2012)

    Article  ADS  Google Scholar 

  25. C. Bruder, R. Fazio, G. Schön, Ann. Phys. 14, 566 (2005)

    Article  MATH  Google Scholar 

  26. H.J. Carmichael, An Open Systems Approach to Quantum Optics, Springer Lecture Notes in Physics (Springer-Verlag, Berlin, 1993)

  27. C.W. Gardiner, P. Zoller, Quantum Noise (Springer Series in Synergetics, Berlin Heidelberg New York, 2004)

  28. C.W. Gardiner, Stochastic Methods: A Handbook for the Natural Social Sciences (Springer Series in Synergetics, Berlin Heidelberg New York, 2009)

  29. D.F. Walls, G.J. Milburn, Quantum Optics (Springer-Verlag, Heidelberg, 2010)

  30. A.J. Daley, Adv. Phys. 63, 77 (2014)

    Article  ADS  Google Scholar 

  31. N. Syassen, D.M. Bauer, M. Lettner, T. Volz, D. Dietze, J.J. García-Ripoll, J.I. Cirac, G. Rempe, S. Dürr, Science 320, 1329 (2008)

    Article  ADS  Google Scholar 

  32. D. Witthaut, F. Trimborn, S. Wimberger, Phys. Rev. Lett. 101, 200402 (2008)

    Article  ADS  Google Scholar 

  33. S. Diehl, A. Micheli, A. Kantian, B. Kraus, H.P. Büchler, P. Zoller, Nat. Phys. 4, 971 (2008)

    Article  Google Scholar 

  34. B. Kraus, H.P. Büchler, S. Diehl, A. Kantian, A. Micheli, P. Zoller, Phys. Rev. A 78, 042307 (2008)

    Article  ADS  Google Scholar 

  35. F. Verstraete, M.M. Wolf, J.I. Cirac, Nat. Phys. 5, 633 (2009)

    Article  Google Scholar 

  36. E. Arimondo, G. Oriolls, Lett. Nuovo Cim. 17, 333 (1969)

    Article  ADS  Google Scholar 

  37. G.J. Yang, O. Zobay, P. Meystre, Phys. Rev. A 59, 4012 (1999)

    Article  ADS  Google Scholar 

  38. G.D. Scholes, T. Mirkovic, D.B. Turner, F. Fassioli, A. Buchleitner, Energy Environ. Sci. 5, 9374 (2012)

    Article  Google Scholar 

  39. A.W. Chin, J. Prior, R. Rosenbach, F. Caycedo-Soler, F. Huelga, M.B. Plenio, Nat. Phys. 9, 113 (2013)

    Article  Google Scholar 

  40. C. Sabín, J. Kohlrus, D.E. Bruschi, I. Fuentes [arXiv:1505.01302] (2015)

  41. J.M. Gerton, C.A. Sackett, B.J. Frew, R.G. Hulet, Phys. Rev. A 59, 1514 (1999)

    Article  ADS  Google Scholar 

  42. T. Kraemer, M. Mark, P. Waldburger, J.G. Danzl, C. Chin, B. Engeser, A.D. Lange, K. Pilch, A. Jaakkola, H.-C. Nägerl, R. Grimm, Nature 440, 315 (2006)

    Article  ADS  Google Scholar 

  43. U. Eismann, L. Khaykovich, S. Laurent, I. Ferrier-Barbut, B.S. Rem, A.T. Grier, M. Delahaye, F. Chevy, C. Salomon, L.-C. Ha, C. Chin [arXiv:1505.04523] (2015)

  44. T. Weber, J. Herbig, M. Mark, H.-C. Nägerl, R. Grimm, Phys. Rev. Lett. 91, 123201 (2003)

    Article  ADS  Google Scholar 

  45. T. Gerike, A scanning electron microscope for ultracold quantum gases, Ph.D. thesis, Johannes Gutenberg-Universität Mainz, 2010

  46. B. Santra, H. Ott [arXiv:1504.00277] (2015)

  47. G. Barontini, R. Labouvie, F. Stubenrauch, A. Vogler, V. Guarrera, H. Ott, Phys. Rev. Lett. 110, 035302 (2013)

    Article  ADS  Google Scholar 

  48. M. Greiner, O. Mandel, T. Esslinger, T.W. Hänsch, I. Bloch, Nature 415, 39 (2002)

    Article  ADS  Google Scholar 

  49. M.J. Hartmann, F.G.S.L. Brandão, M.B. Plenio, New J. Phys. 10, 033011 (2008)

    Article  ADS  Google Scholar 

  50. M. Leib, M.J. Hartmann, New J. Phys. 12, 093031 (2010)

    Article  ADS  Google Scholar 

  51. U. Naether, F. Quijandría, J.J. García-Ripoll, D. Zueco, Phys. Rev. A 91, 033823 (2015)

    Article  ADS  Google Scholar 

  52. H.-P. Breuer, F. Petruccione, The Theory of Open Quantum Systems (Oxford University Press, 2006)

  53. G. Kordas, S. Wimberger, D. Witthaut, EPL 100, 30007 (2012)

    Article  ADS  Google Scholar 

  54. G. Kordas, S. Wimberger, D. Witthaut, Phys. Rev. A 87, 043618 (2013)

    Article  ADS  Google Scholar 

  55. J. Anglin, Phys. Rev. Lett. 79, 6 (1997)

    Article  ADS  Google Scholar 

  56. F. Trimborn, D. Witthaut, S. Wimberger, J. Phys. B 41, 171001 (2008)

    Article  ADS  Google Scholar 

  57. D. Witthaut, F. Trimborn, S. Wimberger, Phys. Rev. A 79, 033621 (2009)

    Article  ADS  Google Scholar 

  58. D. Witthaut, F. Trimborn, H. Hennig, G. Kordas, T. Geisel, S. Wimberger, Phys. Rev. A 83, 063608 (2011)

    Article  ADS  Google Scholar 

  59. H. Pichler, A.J. Daley, P. Zoller, Phys. Rev. A 82, 063605 (2010)

    Article  ADS  Google Scholar 

  60. D. Poletti, J.-S. Bernier, A. Georges, C. Kollath, Phys. Rev. Lett. 109, 045302 (2012)

    Article  ADS  Google Scholar 

  61. D. Poletti, P. Barmettler, A. Georges, K. Kollath, Phys. Rev. Lett. 111, 195301 (2013)

    Article  ADS  Google Scholar 

  62. B. Sciolla, D. Poletti, K. Kollath, Phys. Rev. Lett. 114, 170401 (2015)

    Article  ADS  Google Scholar 

  63. A.J. Daley, J.M. Taylor, S. Diehl, M. Baranov, P. Zoller, Phys. Rev. Lett. 102, 179902 (2009)

    Article  ADS  Google Scholar 

  64. A.J. Moerdijk, B.J. Verhaar, Phys. Rev. A 53, 19R (1996)

    Article  ADS  Google Scholar 

  65. Y. Li, Y. Castin, A. Sinatra, Phys. Rev. Lett. 100, 210401 (2008)

    Article  ADS  Google Scholar 

  66. J.J. García-Ripoll, S. Dürr, N. Syassen, D.M. Bauer, M. Lettner, G. Rempe, J.I. Cirac, New J. Phys. 11, 013053 (2009)

    Article  ADS  Google Scholar 

  67. M. Kiffner, M. Hartmann, New J. Phys. 13, 053027 (2011)

    Article  ADS  Google Scholar 

  68. S. Diehl, A. Tomadin, A. Micheli, R. Fazio, P. Zoller, Phys. Rev. Lett. 105, 015702 (2010)

    Article  ADS  Google Scholar 

  69. G. Watanabe, H. Mäkelä, Phys. Rev. A 85, 023604 (2012)

    Article  ADS  Google Scholar 

  70. R.C.F. Caballar, S. Diehl, H. Mäkel, M. Oberthaler, G. Watanabe, Phys. Rev. A 89, 013620 (2014)

    Article  ADS  Google Scholar 

  71. R. Franzosi, R. Livi, G.-L. Oppo, A. Politi, Nonlinearity 24, R89 (2011)

    Article  MATH  MathSciNet  ADS  Google Scholar 

  72. R. Franzosi, R. Livi, G.-L. Oppo, J. Phys. B 40, 1195 (2007)

    Article  ADS  Google Scholar 

  73. G.S. Ng, H. Henning, R. Fleischmann, T. Kottos, T. Geisel, New J. Phys. 11, 073045 (2009)

    Article  ADS  Google Scholar 

  74. H. Hennig, R. Fleischmann, Phys. Rev. A 87, 033605 (2013)

    Article  ADS  Google Scholar 

  75. E.M. Graefe, H.J. Korsch, A.E. Niederle, Phys. Rev. Lett. 101, 150408 (2008)

    Article  ADS  Google Scholar 

  76. V.S. Shchesnovich, D.S. Mogilevtsev, Phys. Rev. A 82, 043621 (2010)

    Article  ADS  Google Scholar 

  77. F. Trimborn, D. Witthaut, H. Hennig, G. Kordas, T. Geisel, S. Wimberger, Eur. Phys. J. D 63, 63 (2011)

    Article  ADS  Google Scholar 

  78. S. Wimberger, C.A. Parra-Murillo, G. Kordas, J. Phys.: Conf. Ser. 442, 012029 (2013)

    ADS  Google Scholar 

  79. R. Livi, R. Franzosi, G.-L. Oppo, Phys. Rev. Lett. 97, 060401 (2006)

    Article  ADS  Google Scholar 

  80. P. Barmettler, C. Kollath, Phys. Rev. A 84, 041606(R) (2011)

    Article  ADS  Google Scholar 

  81. T. Pudlik, H. Hennig, D. Witthaut, D.K. Campbell, Phys. Rev. A 88, 063606 (2013)

    Article  ADS  Google Scholar 

  82. K.V. Kepesidis, M.J. Hartmann, Phys. Rev. A 85, 063620 (2012)

    Article  ADS  Google Scholar 

  83. V. Penna, Phys. Rev. E 87, 052909 (2013)

    Article  ADS  Google Scholar 

  84. V.S. Shchesnovich, Phys. Rev. A 85, 053616 (2012)

    Article  ADS  Google Scholar 

  85. V.S. Shchesnovich, V.V. Konotop, EPL 99, 60005 (2012)

    Article  ADS  Google Scholar 

  86. C. Ates, B. Olmos, W. Li, I. Lesanovsky, Phys. Rev. Lett. 109, 233003 (2012)

    Article  ADS  Google Scholar 

  87. B. Cui, S.C. Hou, W. Wang, X.X. Yi, J. Phys. B 47, 215303 (2014)

    Article  ADS  Google Scholar 

  88. J. Dalibard, Y. Castin, K. Mølmer, Phys. Rev. Lett. 68, 580 (1992)

    Article  ADS  Google Scholar 

  89. R. Dum, P. Zoller, H. Ritsch, Phys. Rev. A 45, 4879 (1992)

    Article  ADS  Google Scholar 

  90. M.B. Plenio, P.L. Knight, Rev. Mod. Phys. 70, 101 (1998)

    Article  ADS  Google Scholar 

  91. D.K. Campbell, S. Flach, Y.S. Kivshar, Phys. Today 467, 57 (2004)

    Google Scholar 

  92. S. Flach, A.V. Gorbach, Phys. Rep. 467, 1 (2008)

    Article  ADS  Google Scholar 

  93. H. Henning, J. Dorignac, D.K. Campbell, Phys. Rev. A 82, 053604 (2010)

    Article  ADS  Google Scholar 

  94. P.G. Kevrekidis, The Discrete Nonlinear Schrödinger Equation (Springer Tracts in Modern Physics, Springer-Verlag Berlin Heidelberg, 2009)

  95. P.G. Kevrekidis, D.J. Frantzeskakis, Mod. Phys. Lett. B 18, 173 (2004)

    Article  ADS  Google Scholar 

  96. V.A. Brazhnyi, V.V. Konotop, Mod. Phys. Lett. B 18, 627 (2004)

    Article  ADS  Google Scholar 

  97. P. Buonsante, R. Burioni, D. Cassi, V. Penna, Vezzani, Phys. Rev. B 70, 224510 (2004)

    Article  ADS  Google Scholar 

  98. L.E. Reichl, A Modern Course in Statistical Physics (J. Wiley and Sons, New York, 2004)

  99. V.A. Brazhnyi, V.V. Konotop, V.M. Pérez-García, H. Ott, Phys. Rev. Lett. 102, 144101 (2009)

    Article  ADS  Google Scholar 

  100. M. Kreibich, J. Main, H. Cartarius, G. Wunner, Phys. Rev. A 87, 051601(R) (2014)

    Article  ADS  Google Scholar 

  101. D. Dast, D. Haag, H. Cartarius, G. Wunner, Phys. Rev. A 90, 052120 (2014)

    Article  ADS  Google Scholar 

  102. E.-M. Graefe, H.J. Korsch, A.E. Niederle, Phys. Rev. A 82, 013629 (2010)

    Article  ADS  Google Scholar 

  103. E.M. Graefe, U. Günther, H.J. Korsch, A.E. Niedele, J. Phys. A 41, 255206 (2008)

    Article  MathSciNet  ADS  Google Scholar 

  104. V.V. Konotop, D.E. Pelinovsky, D.A. Zezyulin, EPL 100, 56006 (2012)

    Article  ADS  Google Scholar 

  105. D.E. Pelinovsky, P.G. Kevrekidis, D.J. Frantzeskakis, EPL 101, 11002 (2013)

    Article  ADS  Google Scholar 

  106. K. Li, P.G. Kevrekidis, D.J. Frantzeskakis, C.E. Rüter, D. Kip, J. Phys. A 46, 375304 (2013)

    Article  MathSciNet  Google Scholar 

  107. A.S. Rodrigues, K. Li, V. Achilleos, P.G. Kevrekidis, D.J. Frantzeskakis, C.M. Bender, Rom. Rep. Phys. 65, 5 (2013)

    Google Scholar 

  108. D. Dast, D. Haag, H. Cartarius, G. Wunner, Phys. Rev. A 90, 052120 (2014)

    Article  ADS  Google Scholar 

  109. R. Benzi, A. Sutera, A. Vulpiani, J. Phys. A 14, L453 (1981)

    Article  MathSciNet  ADS  Google Scholar 

  110. L. Gammaitoni, P. Hänggi, P. Jung, F. Marchesoni, Rev. Mod. Phys. 70, 223 (1998)

    Article  ADS  Google Scholar 

  111. T. Wellens, V. Shatokhin, A. Buchleitner, Rep. Prog. Phys. 67, 45 (2004)

    Article  ADS  Google Scholar 

  112. A. Vardi, J.R. Anglin, Phys. Rev. Lett. 86, 568 (2001)

    Article  ADS  Google Scholar 

  113. J.R. Anglin, A. Vardi, Phys. Rev. A 64, 013605 (2001)

    Article  ADS  Google Scholar 

  114. I. Tikhonenkov, J.R. Anglin, A. Vardi, Phys. Rev. A 75, 013613 (2007)

    Article  ADS  Google Scholar 

  115. A.J. Leggett, Rev. Mod. Phys. 73, 307 (2001)

    Article  ADS  Google Scholar 

  116. B. Wu, Q. Niu, New J. Phys. 5, 104 (2003)

    Article  ADS  Google Scholar 

  117. L.D. Carr, J. Brand, S. Burger, A. Sanpera, Phys. Rev. A 63, 051601R (2001)

    Article  ADS  Google Scholar 

  118. B. Wu, J. Liu, Q. Niu, Phys. Rev. Lett. 88, 034101 (2002)

    Article  ADS  Google Scholar 

  119. D.J. Frantzeskakis, J. Phys. A 43, 213001 (2010)

    Article  MathSciNet  ADS  Google Scholar 

  120. S. Burger, K. Bongs, S. Dettmer, W. Ertmer, K. Sengstock, Phys. Rev. Lett. 83, 5198 (1999)

    Article  ADS  Google Scholar 

  121. J. Denschlag, J.E. Simsarian, D.L. Feder, C.W. Clark, L.A. Collins, J. Cubizolles, L. Deng, E.W. Hagley, K. Helmerson, W.P. Reinhardt, S.L. Rolston, B.I. Schneider, W.D. Phillips, Science 287, 97 (2000)

    Article  ADS  Google Scholar 

  122. D. Jaksch, V. Venturi, J.I. Cirac, C.J. Williams, P. Zoller, Phys. Rev. Lett. 89, 040402 (2002)

    Article  ADS  Google Scholar 

  123. P. Buonsante, V. Penna, J. Phys. A 41, 175301 (2008)

    Article  MathSciNet  ADS  Google Scholar 

  124. W. Krauth, M. Caffarel, J.P. Bouchaud, Phys. Rev. B 45, 3137 (1992)

    Article  ADS  Google Scholar 

  125. K. Sheshadri, H.R. Krishnamurthy, R. Pandit, T.V. Ramakrishnan, EPL 22, 257 (1993)

    Article  ADS  Google Scholar 

  126. D. van Oosten, P. van der Straten, H.T.C. Stoof, Phys. Rev. A 63, 053601 (2001)

    Article  ADS  Google Scholar 

  127. J. Zakrzewski, Phys. Rev. A 71, 043601 (2005)

    Article  ADS  Google Scholar 

  128. P. Buonsante, V. Penna, A. Vezzani, P.B. Blakie, Phys. Rev. A 76, 011602 (2007)

    Article  ADS  Google Scholar 

  129. P. Buonsante, F. Massel, V. Penna, A. Vezzani, Phys. Rev. A 79, 013623 (2009)

    Article  ADS  Google Scholar 

  130. A.E. Niederle, H. Rieger, New J. Phys. 15, 075029 (2013)

    Article  ADS  Google Scholar 

  131. K. Sheshadri, H.R. Krishnamurthy, R. Pandit, T.V. Ramakrishnan, Phys. Rev. Lett. 75, 4075 (1995)

    Article  ADS  Google Scholar 

  132. M. Snoek, W. Hofstetter, Phys. Rev. A 76, 051603 (2007)

    Article  ADS  Google Scholar 

  133. M. Endres, T. Fukuhara, D. Pekker, M. Cheneau, P. Schauß, C. Gross, E. Demler, S. Kuhr, I. Bloch, Nature 487, 454 (2012)

    Article  ADS  Google Scholar 

  134. A. Rapp, Phys. Rev. A 87, 043611 (2013)

    Article  ADS  Google Scholar 

  135. P. Buonsante, L. Pezzè, A. Smerzi, Phys. Rev. A 91, 031601 (2015)

    Article  ADS  Google Scholar 

  136. Pižorn, Phys. Rev. A 88, 043635 (2013)

    Article  ADS  Google Scholar 

  137. I. Vidanovic, D. Cocks, W. Hofstetter, Phys. Rev. A 89, 053614 (2014)

    Article  ADS  Google Scholar 

  138. P. Buonsante, A. Vezzani, Phys. Rev. Lett. 98, 110601 (2007)

    Article  ADS  Google Scholar 

  139. A.O. Caldeira, A.J. Leggett, Ann. Phys. 149, 374 (1983)

    Article  ADS  Google Scholar 

  140. J.I. Cirac, A. Schenzle, P. Zoller, EPL 27, 123 (1994)

    Article  ADS  Google Scholar 

  141. D.A. Zezyulin, V.V. Konotop, G. Barontini, H. Ott, Phys. Rev. Lett. 109, 020405 (2012)

    Article  ADS  Google Scholar 

  142. V.S. Shchesnovich, V.V. Konotop, Phys. Rev. A 81, 053611 (2010)

    Article  ADS  Google Scholar 

  143. M.J. Werner, P.D. Drummond, J. Comput. Phys. 132, 312 (1997)

    Article  MATH  MathSciNet  ADS  Google Scholar 

  144. A. Sinatra, C. Lobo, Y. Castin, J. Phys. B 35, 3599 (2002)

    Article  ADS  Google Scholar 

  145. A. Polkovnikov, Ann. Phys. 325, 1790 (2010)

    Article  MATH  MathSciNet  ADS  Google Scholar 

  146. B. Berg, L.I. Plimak, A. Polkovnikov, M.K. Olsen, M. Fleischhauer, W.P. Schleich, Phys. Rev. A 80, 033624 (2009)

    Article  ADS  Google Scholar 

  147. F. Trimborn, D. Witthaut, H.J. Korsch, Phys. Rev. A 77, 043631 (2008)

    Article  ADS  Google Scholar 

  148. F. Trimborn, D. Witthaut, H.J. Korsch, Phys. Rev. A 79, 013608 (2009)

    Article  ADS  Google Scholar 

  149. A. Polkovnikov, Phys. Rev. A 68, 053604 (2003)

    Article  ADS  Google Scholar 

  150. J. Dujardin, T. Engl, J. Urbina, P. Schlagheck, Ann. Phys. (submitted) (preprint) [arXiv:1502.02890]

  151. R.A. Pepino, J. Cooper, D. Meiser, D.Z. Anderson, M.J. Holland, Phys. Rev. A 82, 013640 (2010)

    Article  ADS  Google Scholar 

  152. D.B. Gutman, Y. Gefen, A.D. Mirlin, Phys. Rev. B 85, 125102 (2012)

    Article  ADS  Google Scholar 

  153. M. Bruderer, W. Belzig, Phys. Rev. A 85, 013623 (2012)

    Article  ADS  Google Scholar 

  154. L.H. Kristinsdóttir et al., Phys. Rev. Lett. 110, 085303 (2013)

    Article  ADS  Google Scholar 

  155. T. Prosen, Phys. Rev. Lett. 112, 030603 (2014)

    Article  ADS  Google Scholar 

  156. C. Nietner, G. Schaller, T. Brandes, Phys. Rev. A 89, 013605 (2014)

    Article  ADS  Google Scholar 

  157. F.G. Marcos, G. Platero, C. Nietner, G. Schaller, T. Brandes, Phys. Rev. A 90, 033614 (2014)

    Article  ADS  Google Scholar 

  158. G. Kordas, D. Witthaut, S. Wimberger, Ann. Phys., doi: 10.1002/andp.201400189 (2015)

  159. A. Ivanov, G. Kordas, A. Komnik, S. Wimberger, Eur. Phys. J.B 86, 345 (2013)

    Article  ADS  Google Scholar 

  160. M. Naraschewski, R.J. Glauber, Phys. Rev. A 59, 4595 (1999)

    Article  ADS  Google Scholar 

  161. P. Schlagheck, F. Malet, J.C. Cremon, S.M. Reimann, New J. Phys. 12, 065020 (2010)

    Article  ADS  Google Scholar 

  162. M.D. Lukin, M. Fleischhauer, R. Cote, L.M. Duan, D. Jaksch, J.I. Cirac, P. Zoller, Phys. Rev. Lett. 87, 037901 (2001)

    Article  ADS  Google Scholar 

  163. G.-L. Ingold, Y.V. Nazarov, in Single Charge Tunneling, edited by H. Grabert, M.H. Devoret (Plenum, New York, London, 1992)

  164. R.P. Feynman, Rev. Mod. Phys. 20, 367 (1948)

    Article  MathSciNet  ADS  Google Scholar 

  165. H. Kleinert, Path integrals in quantum mechanics, statistics, polymer physics financial markets (World Scientific Publishing Co, 2006)

  166. M. Baranger, M.A.M. de Aguiar, F. Keck, H.J. Korsch, B. Schellhaaß, J. Phys. A 34, 7227 (2001)

    Article  MATH  MathSciNet  ADS  Google Scholar 

  167. A.L. Xavier, M.A.M. de Aguiar, Phys. Rev. A 54, 1808 (1996)

    Article  MathSciNet  ADS  Google Scholar 

  168. M. Stone, K.-S. Park, A. Garg, J. Math. Phys. (NY) 41, 8025 (2000)

    Article  MATH  MathSciNet  ADS  Google Scholar 

  169. E.A. Kochetov, J. Phys. A 31, 4473 (1998)

    Article  MATH  MathSciNet  ADS  Google Scholar 

  170. J.H. Wilson, V. Galitski, Phys. Rev. Lett. 106, 110401 (2011)

    Article  MathSciNet  ADS  Google Scholar 

  171. G. Kordas, S. Mistakidis, A.I. Karanikas, Phys. Rev. A 90, 032104 (2014)

    Article  ADS  Google Scholar 

  172. R.P. Feynman, F.L. Vernon, Ann. Phys. 24, 118 (1963)

    Article  MathSciNet  ADS  Google Scholar 

  173. A.O. Caldeira, A.J. Leggett, Physica A 121, 587 (1983)

    Article  MATH  MathSciNet  ADS  Google Scholar 

  174. K.K. Rajagopal, Physica A 429, 231 (2015)

    Article  ADS  Google Scholar 

  175. J.-H. An, W.-M. Zhang, Phys. Rev. A 76, 042127 (2007)

    Article  ADS  Google Scholar 

  176. M.W.Y. Tu, W.M. Zhang, Phys. Rev. B 78, 235311 (2008)

    Article  ADS  Google Scholar 

  177. W.-M. Zhang, P.-Y. Lo, H.-N. Xiong, M.W.-Y. Tu, F. Nori, Phys. Rev. Lett. 109, 170402 (2012)

    Article  ADS  Google Scholar 

  178. T. Hartmann, J. Michl, C. Petitjean, T. Wellens, J.-D. Urbina, K. Richter, P. Schlagheck, Ann. Phys. (Amsterdam) 327, 1998 (2012)

    Article  MATH  ADS  Google Scholar 

  179. T. Engl, J. Dujardin, A. Argüelles, P. Schlagheck, K. Richter, J. Urbina, Phys. Rev. Lett. 112, 140403 (2014)

    Article  ADS  Google Scholar 

  180. L. Simon, W.T. Strunz, Phys. Rev. A 89, 052112 (2014)

    Article  ADS  Google Scholar 

  181. R. Dubertrand, S. Müller, conference talk, MPIPKS Dresden (2015)

  182. A.R. Kolovsky, A. Buchleitner, EPL 68, 632 (2004)

    Article  ADS  Google Scholar 

  183. A. Tomadin, R. Mannella, S. Wimberger, Phys. Rev. Lett. 98, 130402 (2007)

    Article  ADS  Google Scholar 

  184. C.A. Parra-Murillo, J. Madroñero, S. Wimberger, Phys. Rev. A 89, 053610 (2014)

    Article  ADS  Google Scholar 

  185. M. Lubasch, Quantum Chaos, Entanglement in the Bose-Hubbard Model, Diploma thesis, Heidelberg University, 2009

  186. J. Jing, X. Zhao, J.Q. You, W.T. Strunz, T. Yu, Phys. Rev. A 88, 052122 (2013)

    Article  ADS  Google Scholar 

  187. C. Sias, A. Zenesini, H. Lignier, S. Wimberger, D. Ciampini, O. Morsch, E. Arimondo, Phys. Rev. Lett. 98, 120403 (2007)

    Article  ADS  Google Scholar 

  188. A.U.J. Lode, A.I. Streltsov, K. Sakmann, O.E. Alon, L.S. Cederbaum, PNAS 109, 13521 (2012)

    Article  ADS  Google Scholar 

  189. A.S. Sørensen, L.-M. Duan, J.I. Cirac, P. Zoller, Nature 409, 63 (2001)

    Article  ADS  Google Scholar 

  190. R. Horodecki, P. Horodecki, M. Horodecki, K. Horodecki, Rev. Mod. Phys. 81, 865 (2009)

    Article  MATH  MathSciNet  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Physics Department, Nuclear & Particle Physics Section, University of Athens, Panepistimiopolis, Ilissia, 15771, Athens, Greece

    G. Kordas & A. I. Karanikas

  2. Institute for Energy and Climate Research (IEK-STE), Forschungszentrum Jülich, 52428, Jülich, Germany

    D. Witthaut

  3. Institute for Theoretical Physics, University of Cologne, 50937, Köln, Germany

    D. Witthaut

  4. QSTAR, INO-CNR and LENS, Largo Fermi 2, 50125, Firenze, Italy

    P. Buonsante

  5. S3, CNR Istituto di Nanoscienze, via Campi 213A, 41125, Modena, Italy

    A. Vezzani

  6. Dipartimento di Fisica e Scienze della Terra, Università di Parma, via G.P. Usberti 7/a, 43124, Parma, Italy

    A. Vezzani, R. Burioni & S. Wimberger

  7. Sezione di Milano Bicocca, Gruppo Collegato di Parma, INFN, Parma, Italy

    R. Burioni & S. Wimberger

Authors
  1. G. Kordas
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. D. Witthaut
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. P. Buonsante
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. A. Vezzani
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. R. Burioni
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. A. I. Karanikas
    View author publications

    You can also search for this author in PubMed Google Scholar

  7. S. Wimberger
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to G. Kordas.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Kordas, G., Witthaut, D., Buonsante, P. et al. The dissipative Bose-Hubbard model. Eur. Phys. J. Spec. Top. 224, 2127–2171 (2015). https://doi.org/10.1140/epjst/e2015-02528-2

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1140/epjst/e2015-02528-2

Keywords

Search

Navigation